U.S. patent number 4,470,294 [Application Number 06/433,299] was granted by the patent office on 1984-09-11 for method and apparatus for simultaneous determination of fluid mass flow rate, mean velocity and density.
This patent grant is currently assigned to The United States of America as represented by the United States. Invention is credited to William R. Hamel.
United States Patent |
4,470,294 |
Hamel |
September 11, 1984 |
Method and apparatus for simultaneous determination of fluid mass
flow rate, mean velocity and density
Abstract
This invention relates to a new method and new apparatus for
determining fluid mass flowrate and density. In one aspect of the
invention, the fluid is passed through a straight cantilevered tube
in which transient oscillation has been induced, thus generating
Coriolis damping forces on the tube. The decay rate and frequency
of the resulting damped oscillation are measured, and the fluid
mass flowrate and density are determined therefrom. In another
aspect of the invention, the fluid is passed through the
cantilevered tube while an electrically powered device imparts
steady-state harmonic excitation to the tube. This generates
Coriolis tube-damping forces which are dependent on the mass
flowrate of the fluid. Means are provided to respond to incipient
flow-induced changes in the amplitude of vibration by changing the
power input to the excitation device as required to sustain the
original amplitude of vibration. The fluid mass flowrate and
density are determined from the required change in power input. The
invention provides stable, rapid, and accurate measurements. It
does not require bending of the fluid flow.
Inventors: |
Hamel; William R. (Farragut,
TN) |
Assignee: |
The United States of America as
represented by the United States (Washington, DC)
|
Family
ID: |
23719644 |
Appl.
No.: |
06/433,299 |
Filed: |
October 7, 1982 |
Current U.S.
Class: |
73/32A;
73/861.357 |
Current CPC
Class: |
G01F
1/78 (20130101); G01F 1/8422 (20130101); G01N
9/002 (20130101); G01F 1/849 (20130101); G01F
25/003 (20130101); G01F 1/8427 (20130101) |
Current International
Class: |
G01F
1/78 (20060101); G01F 1/76 (20060101); G01F
1/84 (20060101); G01N 9/00 (20060101); G01N
009/00 (); G01F 001/86 () |
Field of
Search: |
;73/861.37,32A,59 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Report on Blood Flow Measurement, phase 1 report, A. J. Sipin, Apr.
1964, pp. 1-9..
|
Primary Examiner: Kreitman; Stephen A.
Assistant Examiner: Kovalick; Vincent P.
Attorney, Agent or Firm: Lewis; Fred O. Hamel; Stephen D.
Esposito; Michael F.
Claims
What is claimed is:
1. A method of measuring fluid mass flowrate and density, said
method comprising:
providing a straight cantilevered tube,
passing a fluid through said tube,
exciting the fluid-traversed tube to induce transient oscillation
thereof, thus applying harmonic angular velocity to the fluid
particles therein and generating Coriolis forces which act on said
tube to damp the oscillation thereof,
measuring the frequency and decay constant of the damped transient
oscillation, and
calculating the fluid mass flowrate and density from said frequency
and decay constant.
2. A method of measuring fluid mass flowrate, said method
comprising:
providing a straight cantilevered tube,
passing a fluid through said tube from its cantilevered end to its
unsupported end,
exciting the fluid-traversed tube to induce transient oscillation
thereof, thus applying harmonic angular velocity to the fluid
particles therein and generating Coriolis forces which act on said
tube to damp the oscillation thereof,
measuring the frequency and decay constant of the damped transient
oscillation, and calculating the fluid mass flowrate from said
frequency and decay constant.
3. A device for measuring the mass flow rate and density of a
fluid, comprising:
a straight, cantilevered tube having a fixed end portion disposed
to receive said fluid and a freely vibratable end portion through
which said fluid is discharged;
actuating means for deflecting said tube when traversed by said
fluid to induce transient oscillation at the natural resonant
frequency thereof, thereby applying harmonic angular velocity to
the fluid particles traversing said tube and generating Coriolis
forces which act on said tube to provide damped transient
oscillation thereof; and
means for measuring the frequency and decay constant of said damped
transient oscillation of said tube and calculating the fluid mass
flowrate and density from the measured values of frequency and
decay constant.
4. The device of claim 3 further comprising:
an empty, straight, cantilevered reference tube having a fixed end
portion and a freely vibratable end portion and wherein said
actuating means includes means for deflecting said reference tube
to induce transient oscillation thereof and said measuring and
calculating means includes means for measuring the transient
oscillation of said reference tube to calibrate said device.
Description
BACKGROUND OF THE INVENTION
This invention relates generally to methods and apparatus for the
determination of fluid density, mass flowrates, and mean velocity.
More particularly, it relates to measuring such parameters by
subjecting a stream of the fluid of interest to Coriolis inertial
reaction forces. As used herein, the term "fluid" includes not only
homogeneous gases and liquids but also slurries, fluidized
particles, and the like. The invention was made as a result of a
contract with the U.S. Department of Energy.
The state of the art for mass flowmeters of the Coriolis type is
described in the following publications, both of which are
incorporated herein by refernece: K. O. Plache,
"Coriolis/Gyroscopic Flow Meter", Mech. Eng., March 1979, pp.
36-41; W. R. Hamel, "Analysis of Cantilever Coriolis Mass Flowmeter
Concept", (Dissertion; December, 1981), University of Tennessee,
Knoxville, Tenn. Mass flowmeters of the Coriolis type are disclosed
in the following patents to James E. Smith: U.S. Pat. No.
4,109,524, issued Aug. 29, 1978, and U.S. Pat. No. 4,187,721,
issued on Feb. 12, 1980.
Previous flowmeters of the Coriolis type have not been entirely
satisfactory because of instability, mechanical complexity, or
susceptibility to erosion by the fluid being measured.
SUMMARY OF THE INVENTION
Accordingly, it is an object of this invention to provide a novel
method and novel apparatus for directly determining fluid density
and mass flowrates.
It is another object to provide a Coriolis flowmeter which is
relatively insensitive to changes in environmental conditions, such
as temperature.
It is another object to provide an accurate Coriolis flowmeter
which is characterized by straight-through fluid flow.
Other objects and advantages will be made evident hereinafter.
In one aspect, the invention is a new flowmetering method in which
a fluid is passed through a novel Coriolis-type flowmeter
comprising a cantilevered tube which is subjected to
static-deflection excitation. It has been found that the dynamic
response of the cantilivered tube is essentially a second-order
damped response in which the decay constant and frequency of
vibration are dependent on the fluid density and frequency of
vibration, respectively. In accordance with the invention, the
decay constant and frequency of the damped response are measured.
These values then are used to compute the fluid mass flowrate and
density. The mean velocity of the fluid can be determined from the
cross-sectional area of the tube and the flowrate and density.
In another aspect, the invention is a method in which fluid is
passed through the cantilevered tube while an electrically powered
forcing device imparts steady-state harmonic excitation to the
tube, vibrating it at a selected frequency and amplitude. This
subjects the particles of fluid to harmonic angular velocity and
generates Coriolis damping forces acting on the tube. Means are
provided to respond to incipient flow-induced changes in the
amplitude of vibration by changing the power input to the forcing
device as required to sustain the original amplitude of vibration.
The fluid mass flow rate and density then are determined from the
required change in power input.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram of an experimental flowmetering
system designed in accordance with the invention;
FIG. 2 is a graphical mass-flow regression comparison of a
conventional thermal mass flowmeter and a cantilevered mass
flowmeter designed in accordance with the invention;
FIG. 3 is a graph in which the percent difference between (a) the
density of water as calculated in accordance with the invention and
(b) the known density of water is plotted as a function of mass
flowrates as determined with a standard thermal flowmeter;
FIG. 4 is a perspective view, partly in cutaway, of a dual-tube
flow sensor designed in accordance with the invention, and
FIG. 5 is a schematic diagram showing the sensor (FIG. 4) as
mounted to discharge slurry into the headspace of a slurry
receiver.
DETAILED DESCRIPTION OF THE INVENTION
Referring to FIG. 1, the invention will be illustrated as utilized
in an experimental system 7 designed to display the mass flowrate,
density, and mean velocity of a stream of water. The system
included a special flow-sensor tube 9, which was designed and
operated in accordance with the invention. The remainder of the
system consisted of conventional components. As shown, the sensor 9
was incorporated in a flow loop 11 through which the water was
circulated. The loop also included a water reservoir 13, a
temperature indicator 15, block valves 17 and 19, a centrifugal
pump 21, a power supply 23 and Variac control 25 for the pump, a
flow indicator 27, and a standard thermal flowmeter 29 connected to
discharge into an end of the sensor 9. The thermal flowmeter
produced an electrical output proportional to the mass flowrate
therethrough.
In accordance with the invention, the special flow sensor was a
straight tube having a cantilevered portion 10. The cantilevered
tube was composed of stainless steel and had a length of 50.17 cm,
an outside diameter of 9.25 mm, and an inside diameter of 7.5 mm.
One end of the tube was rigidly supported by a bracket 31 and
connected to receive fluid from the thermal flowmeter 29. The
remainder of the tube was unencumbered, so that it might be
vibrated. The outlet end of the tube extended into the headspace
above the water in the reservoir 13. As shown, an A.C. solenoid 33
was mounted adjacent to the canilevered tube to effect
static-deflection motion excitation of the same. That is, when
energized, the solenoid plunger contacted the portion 10 and
deflected it a selected distance (e.g., one cm) from its normal
axial position. When de-energized, the solenoid released portion
10, initiating transient, uniplanar vibration thereof. The solenoid
was actuated by a solid-state relay 34.
Still referring to FIG. 1, a four-arm strain-gage bridge 35 was
mounted on the tube 10 as shown to generate an electrical output
proportional to the magnitude of the vibrations of the tube with
respect to time. As shown, the outputs from the bridge 35 and
thermal flowmeter 29 were fed to amplifiers 37 and 39,
respectively. The amplifier outputs were fed into a realtime
microcomputer system 41 (Model LSI-11, Digital Equipment Co.,),
which was programmed to (a) intermittently excite transient
vibration of the flow sensor 9, (b) record and store
tube-deflection data and thermal flowmeter data; and (c) perform
calibration- and flow-measurement algorithm calculations. As shown,
the microcomputer system generated an output for operating the
relay 34. The system also generated outputs respectively
proportional to the mass flowrate and density of the water in loop
11; these outputs were fed to a digital plotter 43 via s serial
interface 44. The system 41 included a programmable realtime clock
for providing precision date-sampling intervals.
In a typical operation of the system shown in FIG. 1, it was first
determined that the damped vibration of the sensor 9 was unimodal
through 250 Hz. The values for certain calibration constants (to be
described) were then determined, using the thermal flowmeter 29 as
a secondary standard. The water flow through the loop 11 then was
set at ten different values within a flow range of 20:1, and the
statistical averages and standard deviations were calculated for
the constants. With these constants stored in the microcomputer
system, water was circulated through the loop 11 at various rates,
and the mass flowrate diplays for the cantilevered sensor were
compared with the mass flowrates determined with the thermal
flowmeter. The typical flowrate measurement involved establishing
about 1000 data points relating to the vibration-decay curve for
the vibrating sensor tube; this required less than 0.5 sec.
FIG. 2 compares mass flowrate determinations made with the thermal
flowmeter 29 and cantilevered sensor 9 for three separate test
scans. The mass-flow-percent difference is a plot of the variation
of the experimental cantilever Coriolis flowmeter and the thermal
flowmeter coincident readings about a linear regression line
through the entire set of readings. This plot demonstrates the
relative agreement between the two flowmeters. If they were in
perfect agreement, all of the data would fall on the zero-line over
the range of thermal flowmeter readings. As shown, the difference
is within .+-.10% over the full range of measurement. These results
are of the order of the thermal flowmeter itself. It is not
possible from this relative comparison to determine how much of the
.+-.10% was due to either one of the meters. FIG. 3 is a similar
showing relating to the density of water and presents the percent
difference between the density valves determined in accordance with
the invention and the known density of water (997 kg/cm.sup.3),
plotted as a function of the thermal flowmeter output. The density
values based on data obtained with the canilevered tube 9 are
within .+-.2% of the known value over the full range of
measurement.
Referring to system 7 (FIG. 1), when fluid is passed through the
flow sensor 9 while the latter is vibrating in the transient mode,
the angular velocity of the tube and the linear velocity of the
fluid particles relative to the tube combine to generate Coriolis
inertial forces which damp the vibrations of the tube. I have found
that the decay rate of the damped vibration is related to the fluid
mass flowrate and that the frequency of the vibration is strongly
related to fluid density and less strongly related to fluid
velocity. I have also found that the density (.rho.), mean velocity
(U), and mass flowrate (m) of the fluid may be determined by means
of algorithms related to the decay rate and the frequency of the
damped vibrations. The values for .rho., U, and m may be determined
by means of the following algorithms: ##EQU1## where R.sub.1 is the
decay constant of the tube vibration.
R.sub.2 is the frequency of the tube vibration.
R.sub.C1 is the decay constant of the tube vibration with no fluid
flowing (calibrated)
R.sub.C2 is the frequency of oscillation-squared of the tube
vibration with no fluid flowing (calibrated).
K.sub.m is the calibration constant for the mass flowrate.
and where calibration constants a.sub.1, a.sub.2, and K.sub.m may
be calculated as follows, using the thermal flowmeter 29 as a
secondary standard and knowing the density of water: ##EQU2## The
above-referenced dissertation gives the principles underlying these
algorithms and presents examples of software for implementing the
same. The cantilevered Coriolis meter provides mass flowmeter
measurements which are independent of viscosity and pressure.
Pressure pulsations and slugging associated with mass flow
variations will be measured as an average over the length of the
tube.
Tables I and II list various parameters and calibration-constant
values for the above-described runs conducted in system 7.
TABLE I ______________________________________ Parameter
______________________________________ Sensor tube: Outside
Diameter (mm) 9.25 (0.375 in.) Inside Diameter (mm) 7.75 (0.305
in.) *Length (cm) 50.17 (19.75 in.) *Empty Natural Frequency (Hz)
30 *External Damping Coefficient .times. 10 [(N-s)/m.sup.2] 40 [9
lbf-s] /ft.sup.2) Nondimensional .beta. = M/(M = m) 0.2 (*0.16)
Maximum Flow Conditions: *Volumetric flow rate (L/h) 900 (4gpm)
Mean velocity (m/s) 4.9 (16 ft/s) Reynolds number 41,500
______________________________________ *Measured values; other data
are nominal values ; M,m represent masses of fluid and flow sensor
tube 9, respectively, per unit length
TABLE II ______________________________________ Standard Division
Calibration parameter Mean (% of mean)
______________________________________ Channel Biases: Thermal
Flowmeter (kg/h) 2.95098 Cantilever Deflection with flow (V)
-0.03180 empty (V) 0.12604 Calibration Constants: Empty decay
constant, R.sub.Cl (s.sup.-1) 1.070393 3.98 Empty frequency-squared
R.sub.Cl (s.sup.-2) 35,495.9 0.28 a.sub.1 318.5714 0.52 a.sub.2
6.851901 3.08 ______________________________________
FIGS. 4 and 5 depict another embodiment of a cantilevered-tube
flowmeter designed in accordance with the invention. The flowmeter
assembly, designated as 45, includes a protective housing 59, which
is flanged at its inlet end for connection to a tubular coupling
49. The coupling is connected to a process line 47 to receive
slurry therefrom. The other end of the housing extends into the
headspace of a slurry receiver 51. As shown, the housing contains
identical, cantilevered tubes 53 and 55, which are rigidly
supported by a plate 57 closing an end of the housing. Tube 53
serves as a flow sensor and extends through the plate to receive
process fluid from the coupling. Tube 55 is not in communication
with the coupling and serves as an empty reference type.
As shown, the housing 59 contains an electromagnet 61 for
simultaneously inducing transient vibration in the tubes; that is,
the tubes are deflected a selected amount by magnetic and then
released to vibrate freely. The tubes carry respective
vibration-detection means 63 and 65 for generating electrical
outputs proportional to the magnitude of the tube vibrations with
respect to time. These outputs are fed to conventional computer
means for operating the electromagnet 61, storing tube-deflection
data, and performing the above-mentioned algorithm calculations.
The reference tube 55 is exposed to the same environment as tube 53
but is not subject to Coriolis damping forces. The output from the
reference tube is fed into the computer and used to standardize the
metering system with regard to environmental effects. Thus, at all
time the metering system is free from environment-induced
instabilities. This embodiment of the flowmeter may be sized to
permit use of the algorithms presented above.
In another form of the invention, the fluid of interest is passed
through a cantilevered sensor tube (e.g., tube 9, FIG. 1) while an
electrically powered forcing device (e.g., an electromagnetic
actuator) imparts steady-state harmonic excitation to the tube,
vibrating it a selected fixed frequency and amplitude. The
particles of the fluid are subjected to harmonic angular velocity
and generate Coriolis damping forces which act on the tube. Means
are provided to respond to incipient changes in the amplitude of
vibration by changing the power input to the forcing device as
required to sustain the original amplitude of vibration. The mass
flowrate then can be determined from the required change in power
input. This mode of operation is based on my finding that the power
input required to sustain the vibration is proportional to the rate
of change of work done by the damping forces, which are dependent
on mass flowrate. In a system of the kind just described, a
conventional servo-control arrangement would be used to vary the
power input in response to sensed changes in the amplitude of
vibration. The electrical level of the servo-controller output
would be related to total tube damping and hence flow rate. The
system for adjusting the power input to the forcing device may be
similar to that described in the above-referenced article by
Plache. Because this form of the invention utilizes steady-state
excitation of the cantilevered sensor, the algorithms for
calibration and measurement will differ from those presented
above.
The foregoing description of the invention has been presented for
illustrative purposes and to enable others skilled inthe art to
utilize the invention in various embodiments and with various
modifications suited to a particular use. It will be understood
that the illustrated form of the invention is not necessarily the
optimum. Obviously, many modifications and variations are possible
in light of the teaching herein. It is intended that the scope of
the invention be defined by the appended claims.
* * * * *